Joined Common Chords of Napoleon's Circumcircles

What is this about?

An Equilateral Triangle in Napoleon's Circumcircles

Let $ABC',$ $BCA',$ and $CAB'$ be Napoleon's triangles constructed on the sides of $\Delta ABC.$ Choose point $D$ on the circumcircle $ABC',$ pass it through $A$ to the intersection $F$ with $C(CAB')$ and through $E$ to the intersection $E$ with $C(BCA').$

An equilateral triangle in Napoleon's circumcircles

Triangles $DEF$ is equilateral.


The problem is very simple; it submits to chasing inscribed angles.


The solution is outlined in an old variant of this problem.


The problem described on this page stems from an observation of Hirotaka Ebisui.

Napoleon's Theorem

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